Yaw simulator



March 22, 1955 Filed March 4, 1949 W. A. GOOD ET AL YAW SIMULATOR Sheets-Sheet l TIME CLOCK :9 9 i t GENERATOR O 23 1: 1a 7 1 4] SERVO HAVING INERTIA 4 Z SERVO I AND DAMPING I e INTEGRATOR V GIVEN BY EQUATION INTEGRATOR -te IYdt I F*( :0s) 7@s 5* 6):|' s j I 3 5 7 [1dr :1 12 2 n K i J 4 w l M'SSILE RADAR RADAR T gig RECEIVER SIMULATOR 1 r LA L J FIG. I

TANGENT TO FLIGHT PATH INVENTORS: WALTER A. GOOD NORMAN P. HEYDENBURG A TTOR/VEY United States Patent F YAW SIMULATOR Walter A. Good, Silver Spring, and Norman P. Heydenbur Kensington, Md.

Application March 4, 1949, Serial No. 79,666

25 Claims. (Cl. 244-14) The present invention relates to a simulator which predicts the yaw course and yaw dynamics of a guided missile that is following a beam of radio-frequency energy directed at a fixed target.

One of the principal objects of the invention is to provide a simulator which will function to reproduce the dynamics of a roll-stabilized guided missile in flight.

Another object is to provide a yaw simulator,"which consists of a combination of mechanical and electronic components of known design, for reproducing the yaw conditions of a guided missile.

Other objects and many of the attendant advantages of this invention will be appreciated readily as the same becomes understood by reference to the following detailed description, when considered in connection with the accompanying drawings, wherein:

Figure l is a 'block diagram of an improved yaw simulator;

Figure 2 is a diagrammatic view showing the angles of yaw with respect to the flight path of a guided missile; and

Figure 3 is a combined electrical and mechanical diagrgm corresponding to Fig. 1, showing the circuits use Heretofore there has been no satisfactory way of determining the yaw characteristics of a roll-stabilized guided missile, designed to follow a beam of radiofrequency energy that has a fixed direction, commonly known as a radar beam, except actual flight-testing of such missile. Since each such test results in the destruction or loss of an expensive missile, and moreover is very wasteful of time, because progress can be made only by building a succession of missiles, each incorporating the lessons learned from the testing of its predecessor, it is very desirable to provide a more expeditious and less wasteful procedure for securing the desired information.

This is accomplished by the present invention, which makes it possible to ground-test the missile, and thus determine its yaw characteristics without the necessity of an actual flight test, and hence without loss of the missile. In order to make this ground-testing possible, the invention contemplates the provision of an apparatus that simulates the missile, as to the desired characteristics, and in which the yaw-responsive control means of the missile may be subjected to suitable tests. Because of the numerous parameters that must be considered, it is necessarily a somewhat complicated matter to take proper account of them all, but for practical purposes certain approximations may be made which greatly simplify the procedure, as will be explained hereinafter.

It is desirable, in carrying the invention into effect, that the following equations, describing the dynamics of the missile in yaw, be simulated:

6=wing angle (wing used for steering in yaw);

. 2,704,644 Patented Mar. 22, 1955 'y, 'y, a, a, R, 0 designate first and second derivatives of' ,a,Rand6;

0=angle between the reference line and the line that passes through the origin and through the center of gravity of the missile;

a=yaw angle or angle of attack of missile body;

R=range of missile;

V =at\l/1erage velocity of missile along tangent to as=proportional to slope of total lift curve;

e=6ITOI angle of missile from radar beam;

a4=proportional to slope of wing lift curve;

a5=yaw damping coeflicient;

as=spring constant of stiffness;

a7=coefiicient of forcing function; and

firi angle between the target direction and the reference.

me. a

To simplify the equations and therebycorrespondingly simplify the apparatus required, certain changes and approximations were made, as follows: Each of Equations 1 and 2 was solved for o: and the two expressions thus obtained were equated], giving Equation 6 free from a but still containing its first two .deriw atives a and ii. 7

By differentiating Equation 1 twice successively, expressions for these two derivatives were obtained as fol lows:

:11-22 and 13:?

Upon substituting them in Equation 6 there results Equa tion 7, which is free from on and its derivatives.

If 6 is changing at a frequency below three cycles per second, the terms in 5 and 6 become negligible in com parison with f6dt. Hence they are omitted in the present simulator. A

Upon integrating there results (9) t6=fVdt+C When the target is fixed, it is convenient to move the reference line into coincidence with the radar beam, that is, to make 0r=0. Then 6 becomes equal to 0, and hence only 0 need be considered here. i

In the present simulator the following values of the coefiicients have been used, based on a missile whose center of gravity is at a 50% chord position, that is, the center of gravity is located at a distanceof one-half the wing chord from the leading edge of the steering wings:

Upon substituting these values in Equation 8 it becomes =angle between the tangent to the flight path and a so Upon using another notation, wherein p and p denote reference line;

the first and second derivatives respectively, the general and this form appears in block of Fig. 1'.

. The present. system simulates: a: beam. rider. that is, a self-propelled guided missile which is following or .riding a radar beam directed. at a fixed target. The simulator has been calibrated with a givenset of coefficients representing a typical guided: missile. The coeflicients were derived. from wind tunnel data. and other sources. The complete steering: loop shown in Figure 1 includes, among: other components, the radar simulator, a radar receiver and a conventional hydraulic servo which operates: the: yaw control wings, and which may be of any suitable type, for example, like those used in automaticpilots for aircraft- Tests have. been run to determine the type of control function requisite for the wing servo, in order that it may provide a stable radar-beam rider. Preliminary results have shownthat the control function must include the derivative of the error signal in addition to the error signal itself. The value of the: ratio. of the error angle to the wing. displacement angle and the amount of derivative control, can be determined by observing the error angle during. a simulated flight, with a given set of initial values of the angles,

, The manner in which the equations have been simulatedis shown in Figures 2 and 3. Starting. with the wing angle, an integral is formed by using a conventional mechanical sliding-ball-and-disc integrator of the type used in fire control computers. A- servo-has been employed to represent the left-hand side of Equation 10, since' this is also the equation of a servo system having inertia and damping. For the specific values of the coefficients appearing in Equation the servo must have an actual frequency of 2.3 cycles per second, and a damping of onefifth. the critical value. p

First considering; Fig. 1 and. starting. at a convenient but arbitrary point of the loop, namely the servomotor 1, which may suitably be a hydraulic motor, the loop will be. .traversedtin.aclockwise: sense. It should be noted that this servomotor I as well as the radar receiver 15, is carried by, and forms part of, the missile 'M.

The output of the servo motor 1, which is a mechanical shift of a piston rod, ofextent proportional to. the: angle 6.. is fed through a suitable mechanical connection 2, to themechanical' integrator 3. This is a mechanism wherein a disc or the like rotates. at constant. angular velocityand a sphere resting on said disc is shifted radially, in accordance with the deflections introduced by the connection 2. This sphere is also in-contact witha rotatable. cylinder, and turns the latter at a variable speed, dependent on the radial-distanceof the sphere from the axis of rotation of said disc. 3 This motion: is. then conveyed to the: servo system 5 through the mechanical connection. 4. In. one sense, this servo S'may be. considered as: one of the computing. elements of' the system. The system 5 has inertia and damping given by the; equation d f g+os+anfi+ am+am= where is the rate, or derivative of. "ywith respect to time, and dt the corresponding second derivative;v the" other symbols having the meanings: already defined. This system 5 solves. the-above equation, giving the value of the'angle' 'y.

ontputof'servos in t'urn is'fed, through mechanieal f connejetion- 6, into a second integratorl mechanically similar'tointegrator3, which gives an output f'ydt, thatis' fed through connection 8 into the servo 11.

This: servo 11: is'also supplied-with a second input, from the clock 9,. through the electrical connection 10. This cl'oc need not be a conventional timepiece, but merely a good constant; speed motor or equivalent device. From the combined inputs,,frydt and t,, there is obtained the angle 3;, which fed through electrical, connection. 12.. t'o'the radar simulator 13 to control the pulse modulation of the same, as to both magnitude and phase.

The simulated radar signal produced by 13 is fed to the radar receiver 15, carried by the missile, through the electrical connection 14, and this receiver 15 in turn, through the electrical connection 16, transmits the proper adjustment to servo 1, that is, the simulated yaw steeringvane setting.

A derived assembly, comprising elements 17 to 23 inclusive, may also be provided, to give an indication of the instantaneous value of the angle a. This assembly which, in contrast to servo 5, may be considered as a mere follower or repeater, consists of the mechanical connection 17 which supplies motion representing the value of angle 6 to the servo 21, in conjunction with the generator 19, rotated at a speed proportional to angle '7 by the mechanical connection 13, and supplying an output which is proportional to the derivative of said angle to the servo 21, through the electrical connection 20. The servo 21 combines these inputs, in accordance with the equation supplying the resultant to the a-dial 23, through shaft .22; The definitions of the various angles have already been given. The angles themselves are shown in Fig; 2.

Referring now in detail to the'system, and still keeping in mind Fig. 1 for general reference, attention is called to Fig. 3. As before, the conventional missile hydraulic servo 1' is shown merely as a block diagram. Through the mechanical connection 2, this actuates the conven-' tional mechanical integrator 3, which includes the disc 24, kept in uniform rotation by the constant speed motor 25; through the speed reducing gears 26 and 27. Suitably mounted spheres 28 are shifted radially of said disc 24 by a rack bar 29 in mesh with a pinion 30 actuated through gearing 31 from the shaft 2; A dial 32, which say be graduated to indicate the value of angle 6, is also actuated by the same shaft 2, through suitable gearing if necessary.

The integrator 3 includes also the cylinder 33 which is rotated by the upper sphere 28'. The rotary motion of this cylinder is transmitted through the mechanical connection 4, comprising the speed-reducing gears indicated, to. the servo which is indicated as a whole by block 5 of Fig. 1,, and which in detail comprises elements 34' to 58 inclusive of Fig. 3. The element 4 also operates dial 125, which indicates the value of the expression (a4as+a'z)f6a't. I

A potentiometer 34, having the rotatable contact arm 35', is electrically energized, through resistors 36 and 37, by the secondary winding 38' of a transformer 39, whose primary winding 40 is fed from a volt alternatingcurrent source, as shown. A second potentiometer 41, with the rotatable contact arm 42, is likewise energized by said winding 38. A dial 43', carried by the same shaft 6 that actuates the contact arm 42,.indieates the instantaneous values of the angle An electrical circuit is provided by the conductors 45 and. 46, connected to the arms 35 and 42 respectively, and is connected to the input side of, amplifier 47' and thence. through conductor 48' to the output side of a damping generator 49, whose excitation is derived through conductors 50 and 51 from. a suitable source 52 of; ad justable. alternating voltage which may include a potentiometer.- 53 and an isolation transformer 54', energized from the. alternating currentmains, as shown.

The damping generator 49 is actuated mechanically by the shaft 55 of Z-phase motor 56, one phase of which is energized from the supply mains, while the other is operated electrically by the output of amplifier 47,.through conductors 57 and 58. Shaft 55' drives shaft 6 through gearing 44. To simulate damping; this generator 49 provides a voltage opposing that. of. the remainder of the circuit, and thus tends. to reduce; the amplifier input voltage to zero more quickly when a balanced condition is approached.

The next device in the loop is the integrator 7 of Fig; 1, (elements 59-76 inclusive of Fig. 3) which in Fig. 3 is seen to comprise a constant speed motor 59 which, through the pinion 60 and gear 61, rotates the disc 6?. upon which rest the spheres 63. These spheres cause the cylinder 64 to turn' at a rate determined, by the angular velocity of the disc and: the radial position ofthe spheres,

which in turn is determmed by the rack bar 65, controlledby the pinion 66, rotated by the shaft 6, also shown in Fig. 1. Incidentally, a single constant speed motor is usually used in actual practice in place of two motors, 25 and 59, the two being shown separately merely to simplify the drawing.

Through suitable gearing 67 this cylinder 64 operates the shaft 68 which turns the contact arm 69 of a potentiometer resistor 70, whose terminals 71 and 72 are supplied with current from the center-tapped secondary winding 73 of an isolation transformer 74 whose primary winding 75 is supplied at a suitable voltage from an autotransformer 76 energized from the alternating power source.

The next unit in the loop is the servo 11 of Fig. 1,

comprising elements 77-93 and 126-131 inclusive of Fig. 3. The 2-phase servo motor 77 has one phase supplied from the mains, while the other is operated from the output leads 78 and 79 of an amplifier 80 whose input leads 81 and 82 are connected respectively to the rotatable contact arm 83 and one end of the resistor 84 of a potentiometer, whose other end is connected by conductor 85 to the shaft 68 of the arm 69, already described.

The shaft 86, of servomotor 77, through suitable gearing 87, operates shaft 12. This shaft carries a dial'88 which is graduated to show the value of angle 0, the socalled error angle. In this connection, it should be remembered that c has been made equal to 0, by making the radar beam coincide with the reference line, Fig. 2. It will be noted that shaft 12 also constitutes a part of the conductor 82 which turns the contact arm 89 whose end moves along the potentiometer resistor 90. The terminals of this resistor 90 are connected to the ends of center-tapped secondary winding 91 of a transformer 92 whose primary winding is 93. A conductor 8 connects thesaid center tap to the center tap of winding 73.

A damping generator 126 is operated by the shaft 86. This generator derives its excitation from an autotransformer 130 connected to the alternating current mains. Conductor 131 leads directly to the field of generator 126, while the other terminal of said field is connected by conductor 128 to a variable tap on the transformer winding 129. The output voltage of this damping generator 126 is placed in series-opposition with the input of the amplifier 80, through conductors 82 and 127. This provides the necessary opposing voltage in the said input circuit to prevent the servomotor 77 from overshooting the zero position.

The next unit to be described is that designated as a whole as the clock 9 in Fig. 1, and which comprises the elements 94-100 of Fig. 3. The clock 94 itself is here shown as a motor having a shaft 95 that rotates at the rate of one revolution per minute. Through a manually controlled disc-clutch 96, this shaft drives the shaft 97 that carries the time dial 98, graduated, in this specific case, -52 seconds. The shaft 97 operates the contact arm 83, already described, and also operates the contact 99 that slides along the autotransformer winding 100, which is connected across the alternating current mains, as shown. A conductor completes the circuit, so that thus the voltage supplied to the winding 93 of transformer 92 is a function of time. Wires 10 and 10a of Fig. 3, jointly constitute the equivalent of the single connection 10 of Fig. l.

The shaft 12 turns the contact arm 123 that moves along the potentiometer resistor 124 which is connected across conductors 12b and 120, which jointly with conductor 12a, connect the shaft 12 to the radar simulator 13.

The detailed structures of radar simulator 13, radar receiver and hydraulic servo 1, together with their interconnecting means 14 and 16, constitute no part of the present invention, hence are not described in detail.

The remaining assemblage is that appearing at the top of Fig. 3, and including the devices 1723 inclusive of Fig. .1, which. relate to means for indicating the value of angle at. These are shown in detail as a shaft 17 which operates the contact arm 101 that moves along the potentiometer resistor 102, across which, a suitable voltage is maintained by the center-tapped secondary winding 103 of a transformer 104, whose primary winding 105 is energized from the mains.

Conductors 106 and 107,, connected respectively to 6 the center tap of winding 103 and to the contact arm 101, convey the output of the potentiometer 101, 102 to the input side of an amplifier 108, through the output, winding of a generator 19, which is operated by shaft 18, mechanically geared to the shaft 55, and through another potentiometer, as follows:

A transformer 109 has its primary winding 110 energized by the alternating current mains, as shown, its secondary winding 111 having a center tap connected to conductor 106. The terminals of the winding 111 are connected to the ends of the potentiometer resistor 112, whose contact arm 113 is connected by conductor 114 to one input terminal of the amplifier 108, the other input terminal thereof being connected to one of the output terminals of the generator 19 by conductor 115. This generator, whose purpose is to provide a voltage representative of which is one of the components that must be fed into the amplifier 108 in order that the equation thatyiclds amay be solved by the assemblage, receives its field excitation from the alternating current mains, throughthe transformer 116 whose secondary winding 117 is connected to the generator 19 as shown.

The output terminals of the amplifier 108 are connected to excite one phase of the 2-phase servo motor 118 through conductors 1-19 and 120, the other phase being energized directly from the mains. motor 118, through gearing 122, operates shaft 22 which rotates the contact arm 113 and also the dial 23, which indicates the instantaneous values of the angle on.

The operation of the apparatus is as follows, referring more particularly to Fig. 3: a

A definite value of 6, the wing angle of the'wing "used for steering in yaw, is set on the fi-dial 32, by the servo 1, in response to a radar signal.

This causes the spheres 28 of the mechanical integrator 3 to assume a corresponding setting, and thereby the cylinder 33 is set into rotation to cause the ffidt dial to give a reading proportional to the value of the integral. The gearing 4 that operates said dial also controls the potentiometer arm 35, which in turn feeds into ampli-' fier 47 a voltage representing the value of said integral.

However, this voltage is opposed. by that derived from the potentiometer arm 42 which is controlled by the shafts 55, 44, and 6 that also operate the -'y-dial 43, which indicates the angle between the tangent to the flight path and the reference line. The damping generator 49 is also in the same amplifier-input circuit, with the object of balancing the potentiometers more rapidly and closely.

The same shaft 6 adjusts the spheres 63 of the integrator 7, whose mechanical output controls the motion of potentiometer arm 69, which, in conjunction with thepotentiometer 89, 90, provides the input voltage of amplifier 80. The potentiometer 83, 84, which -is the automatic gain control of amplifier 80, is operated by the constant speed motor 94, and thus yields a voltage. that is a function of time. The potentiometer 89, 90, on, the other hand, is operated by the servo motor 77 which deri1\f/es one of its phases from the output of amplifier 80 itse t The servomotor 77, which derives excitation for one of its phases from the amplifier 80, will turn the 0-dial 88, through the shaft 12 geared to said motor and'will thus cause said dial 88 to indicate the error angle 0, in addition to adjusting the arm 123 of the potentiometer 123-124, which controls the radar simulator 13, to give the appropriate output signal to the receiver 15. Thus, forany wing angle 6 set. into the dial 32, they dial 88 will show the resulting error angle 0.

A simulated radar device for use in the invention may be of the type in which the signal produced is composed of a series of pulses. These pulses may be modulated by a sinusoidal envelope, the relative polarity (or phase) and amplitude of which depends upon whether the angle of yaw is to the right or left of center or, if the angle of attack response is being measured, whether the angle of attack is above or below the beam course.

The frequency of repetition of the pulses ofthe simulated radar signal may be relatively low as compared with the frequencies employed in actual. radar.. The

The shaft 121 of,

radar simulator 13- of. Figure 3 is designed so that when comprises an unmodulated series of pulses of uniform.

amplitude.. When. the 0. dial is moved to correspond. to an error angle of one direction, the simulated radar pulses are amplitude; modulated by a sinusoidal envelope the amplitude of which. depends on the magnitude of the error angle. Whenthe error angle is in: the opposite direction the modulation envelope will be inverted or reversed in polarity.

The above described simulated radar signals are of the character of a'ctualsignals which might be received in an aircraft, such as a guided missile, in actual flight as it rides th'ebeam which determines its course of travel The transmitter emits a pencil beam of. constant amplitude R. F. energy which is nutated to describe a cone having its apex at the transmitter. The rate of nutation may be of the order of 30 cycles per second. It will be apparent that if the receiving antenna on the guided aircraft is on the axis of the above described cone the received signal will be unmodulated. However, if the airera'ftlis on one side of the axis the R. F. si nal will be ampl-itude modulated at a sine wave rate of 30 cycles per second; on the other side of the axis, the modulationsare electrically inverted or 180 displaced in phase.

It should be borne in' mind. however, that the above describes only one form of this component of the invention which suitably simulates one system of radar for which the radar receiver is designed. The radar simulator is, of course, designed to complement the radar receiver 15 whether the latter is an actual or simulated component. A-ny radar transmitter and receiver, actual or simulated, by means of which the variations in theerror angle registered by dial 88 can control the missile hydraulic servo 1 comes Within the perview of this invention.

The constants for any particular missile'to be tested are set into the system by proper adiustrnent of the voltages it'was desi ned tocompute on a one-to-one" time scale,

thus making it possible touse actual components of the missile (receiver, etc.) without change, to complete the control loop;

It should be noted that yaw and pitch are exactly the same in" nature except that one is horizontal and the other vertical; so thatwith proper connections to the simulated test apparatus the same simulator device can be used to test b'oth yaw and angle of attack dynamic characteristics. For this reason it will be understoodthat wherever the word yaw appears in the specification or claims herein, it encompasses the steering of the missile iirboth horizontal and vertical directions since the Words an le of attack would be equally appropriate.

Obviously many modifications and variations of the present invention are possible in the light of the above teachings. It is therefore to be understood that within the scope of the appended claims the invention. may be practiced otherwise than as specifically described.

What is claimed is:

1. A-device for determining the dynamic steering characteristics of a guided aircraft, said device comprising a follow-up control circuit to simulate a flight test Without requiring. actual flight, said follow-up control circuit including'grounded steering means for said aircraft, a device produc'ing'simulated radarsignals, means modulating said signals in response to deflection of said steering means and receiving means for said simulated radar signals, the output of'said' receiving means controlling said steering means in a manner to correct for errors in the simulated flight of said aircraft.

2". A device as described in claim 1 in which said follow-up control circuit includes a component having inertiaand" damping equivalent" to those of the aircraft.

3 A device for determining the dynamic steering characteristics of a guided aircraft, said device comprising a follow-up control circuit to simulate a flight test without requiring actual flight,- said'follow-up control circuit including'rg'rounded steering means for said aircraft, adevice producing simulated radar signals, means modulating said signals im-response to deflection of said steering means 8 andv receiving;rnea-ns for said 'simul'atedradar signals, outputof said receiving means controlling sa1d stee r1ng. means in amanner to correct for errors in theslmula'ted flight of said aircraft as indicated by said simulated. radar;

signals; I

4. A device for determining the dynamic steering. char-'- acteristics of a guided aircraft, said device comprisingafollow-up control circuit to simulate aflight test without requiring actual. flight, said follow-up control circuit in cluding grounded steering means for said aircraft, a device producing simulated radar signals, means. causing said signals to be modulated in response to deflection 'of. said= steering means and receiving means for said simulated:

radar signals, theoutput of saidreceiving means control:-

ling said steering means in a manner to correct for errors in the theoretical flight of said aircraft as indicated. by said simulated radar signals.v 5. A device as described in claim 4 follow-up control circuit includes a component; having: inertia and damping equivalent to those of the aircraft.

6. A simulator for. predictingthe yaw course of: a guided. missile that contains a steering servo-mechanism and a; radar receiving device for controlling said servo mecha' nism, said simulator comprising a follow-up control loopcomprising; in series relationship in the order named, means to integrate the output. of said steering servo mechanism; a second servo-mechanism having inertia and damping equivalent to those of the missile, a second integrating means integrating the output of said second servo mechanism, a third servo-mechanism and a modulat'able device producing electrical signals resembling radar signals, said radar receiving device and said steering servomechanism.

7. The device described in claim 6 including means to indicate the instantaneous value of the yaw angle of the l'IllSSl e.

8. The device described in claim 7 in which the means to indicate the instantaneous value of the yaw angle of the missile comprises a fourth servo energized by two combined inputs, one proportional to the output of said steering servo-mechanism and the other proportional to the derivative of the output of said second servo-mecha- 1118111.

9. A- device as described in claim 8 in whichthe'inertia and dampingcharacteristics of said second servo mec'ha nism are given by the equation:

where P and P represent the first and second derivatives respectively of the equation:

as=coeflicient proportional to the slope of. the total lift curve a5=yaw damping coeflicient as=spring constant of stiffness v =angle between the tangent to the flight path' and-a reference line and =tirst and second derivatives of 1 respectively 6=angle of deflection of wing for steering.

10. The device descrimed in claim 9. in which said'fourth servo combines the inputs thereto in accordance with. the equation:

'y"-a 6 s where a=value of the yaw angle of the missile -9=h derivative of the angle between the tangent. to the flight path and a reference line a3=coefficient proportional to the s'lopeof the total lift curve I a4=coeflicient proportional to the slope of the wing lift curve 5=angle of deflection of wing for steering.

11. A device for determining the steering'characteristics of a guided missile without actual flight test comprising a follow-up control circuit, said circuit comprising in series a steering servo, means to integrate the movement of in which same.

i i-Maid;

the steering servo, a Second servo means having predetermined inertia and damping characteristics, said second servo means being energized in proportion to the integral of the said steering movement, means to integrate the output of said second servo means, a third servo means energized in proportion to the integral of the output of said second servo means, means producing simulated radar signals modulated in accordance with the output of said third servo means, receiving means receiving the output of the signal producing means, the output of the receiving means controlling said steering servo in a direction to correct for errors in the simulated course of flight of said missile.

12. The device described in claim 11 including means to indicate the instantaneous value of the yaw angle of the missile.

13. The device. described in claim 12 in which the means to indicate the instantaneous value of the yaw angle of the missile comprises a fourth servo energized by two combined inputs, one proportional to the output of said steering servo and the other proportional to the derivative of the output of said second servo means.

14. A device as described in claim 13 in which the inertia and damping characteristics of said second servo means are given by the equation:

where P and P represent the first and second derivatives respectively of the equation:

aa=coetficient proportional to the slope of the total lift curve a=yaw damping coeificient as=spring constant of stiffness 'y=angle between the tangent to the flight path and a reference line 7 and -y=first and second derivatives of 7 respectively 6=angle of deflection of wing for steering.

15. The device described in claim 14 in which said fourth servo combines the inputs thereto in accordance with the equation:

where a=value of the yaw angle of the missile =the derivative of the angle between the tangent to the flight path and a reference line =coeificient proportional to the slope of the total 11ft curve a4=c0eflicient proportional to the slope of the wing lift curve 6=angle of deflection of wing for steering.

16. A device for determining the dynamic steering characteristics of a guided missile without actual flight test comprising a follow-up control circuit, said circuit comprising in tandem relationship a missile steering servo, means to integrate the steering displacement of said steering servo, a second servo means having predetermined inertia and damping characteristics, said second servo means being energized in proportion to the integral of the steering displacement of said steering servo, means to integrate the resulting movement of said second servo means, a third servo mechanism controlled and actuated in proportion to the integral of the movement of said second servo mechanism, means simultating radar signals modulated in accordance with the movement of said third servo mechanism, radar receiving means receiving the output of said means simulating radar signals, the output of said receiving means controlling said steering servo in a manner to correct for errors in the simulated course of flight of said missile with respect to a theoretical directional guiding beam of radiation.

17. The device described in claim 16 including means to indicate the instantaneous value of the yaw angle of the missile.

18. The device described in claim 17 in which the means to indicate the instantaneous value of the yaw angle of the missile comprises a fourth servo energized by two combined inputs, one proportional to the output 1b v of said steering servo and the other proportional to the derivative of the output of said second servo means.

19. A device as described in claim 18 in which the inertia and damping characteristics of said second servo means are given by the equation:

. respectively of the equation:

as: coefficient proportional to the slope of the total lift curve as -yaw damping coeflicient aezsprmg constant of stiffness 7=angle between the tangent to the flight path and a reference line.

{I and yzfirst and second derivatives of 7 respectively 5=angle of deflection of wing for steering.

20. The device described in claim 19 in which said fourth servo combines the inputs thereto in accordance with the equation:

where a=value of the yaw angle of the missile "y=the derivative of the angle between the tangent to the flight path and a reference line aszcoefficient proportional to the slope of the total lift curve aa coeflicient proportional to the slope of the wing lift curve 6=angle of deflection of wing for steering.

21. A device for determining the steering characteristiccs of a guided missile without actual flight test comprising a follow-up control loop, said loop comprising in series a steering servo, means to indicate the output of said steering servo, means to integrate the output of said steering servo, means to indicate the integral of the output of said steering servo, a second servo means having predetermined inertia and damping characteristics, said second servo means being energized in proportion to the integral of the output of said steering servo, means to indicate the output of said second servo means, means to integrate the output of said second servo means, a third servo means energized in proportion to the integral of the output of said servo means, means to indicate the output of said third servo means, means producing simulated radar signals modulated in accordance with the movement of said third servo means, receiving means for the output of the signal producing means, the output of said receiving means controlling said steering servo so as to correct for errors in the direction of simulated flight of said missile.

22. The device described in claim 21 including means to indicate the instantaneous value of the yaw angle of the missile.

23. The device described in claim 22 in which the means to indicate the instantaneous value of the yaw angle of the missile comprises a fourth servo energized by two combined inputs, one proportional to the output of said steering servo and the other proportional to the derivative of the output of said second servo means.

24. A device as described in claim 23 in which the inertia and damping characteristics of said second servo means are given by the equation:

where P and P represent the first and second derivatives respectively of the equation:

and

aa=coeflicient proportional to the slope of the total lift curve a5=yaw damping coeificient as=spring constant of stifiness yzangle between the tangent to the flight path and a reference line 7 and 'yrzfirst and second derivatives of 7 respectively 6=angle of deflection of wing for steering.

I 1 2 r .25. The device rdescribed in claim .24 in, which: said.

fourth servocoinbines the-inputs 'thez'eto ih-abcb'r'd'ai'lce. I eursge 1 with theequatien'z aiangiedfrdeflefcfibn'atvwinggtfot 'ste'eriiig,

1 5' References Citedin the'fiiefo'f 'thi'sip'atent where UNITED-STATES PATENTS I x 2448,0107 ,Ayres: Aug.,311', 1948' azva'lueof the yaw angle of the misslle 2 557,401 Agi g 15 1; l n 19, 1951.1,

=the derivative of the angle between the tangent to the 10 1 3 gh 1360- ;v flight path and a referenceline 7 a3=coefficient proportional to the slope of the total lift curve u cqeflicientwgmporfiunal {tothe slope of theiwing lift.- 

